Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

Ariel Edery

Published Jan 1, 2005• 14 citations
OpenAlex

Abstract

Recently, the Casimir pressure was calculated for infinitely thin and infinitely repulsive parallel plates due to quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate (BEC). We generalize this result and obtain an expression for the Casimir pressure in a three-dimensional rectangular cavity with Dirichlet boundary conditions and arbitrary lengths. We then calculate finite size corrections to the parallel plate scenario.

Related papers

Casimir forces in Bose–Einstein condensates: finite-size effects in three-dimensional rectangular cavities

Ariel Edery

The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.

arXiv:hep-th/0510238•Journal of Statistical Mechanics Theory and Experiment•Jun 8, 2006•27 citations

Casimir energy of a BEC: from moderate interactions to the ideal gas

Jürgen Schiefele, Carsten Henkel

Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.

arXiv:0809.1816•Journal of Physics A Mathematical and Theoretical•Dec 17, 2008•27 citations

On the Bogoliubov theory: Casimir effect in a single weakly interacting Bose gas at zero-temperature with Neumann boundary condition

Phạm Thế Song

Developing Bogoliubov theory of weakly interacting Bose gas in uncompacted three-dimension space, quantum fluctuation energy of one component dilute gas of Bose-Einstein condensate (BEC) confined to two parallel plates investigated at zero-temperature in grand canonical ensemble (GCE) with Neumann boundary condition (BC). The Casimir force considered in comparison to the one with Robin BC, Dirichlet BC and periodic BC.

arXiv:2006.11596•Jun 20, 2020•1 citation

Casimir force on an interacting Bose–Einstein condensate

Shyamal Biswas, Jayanta K. Bhattacharjee, Dwipesh Majumder +2 more

We have presented an analytic theory for the Casimir force on a Bose–Einstein condensate which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wavefunction as well as for the phonon field. We have shown that the condensate wavefunction (which obeys the Gross–Pitaevskii equation) is responsible for the mean field part of the Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.

arXiv:0907.2616•Journal of Physics B Atomic Molecular and Optical Physics•Apr 6, 2010•28 citations

Casimir forces in a quasi–one-dimensional trapped dilute Bose gas

Xiao-Lu Yu, Ran Qi, Zhibing Li +1 more

We discuss a Casimir force due to zero-temperature quantum fluctuations in an interacting quasi–one-dimensional Bose-Einstein condensate (BEC). For the first time, we can investigate the effect of the trapping potential and the atom-atom interaction simultaneously both of which contribute to the Casimir force. Furthermore, we calculate the Casimir force due to thermal fluctuations at finite temperature. Finally, we speculate on some possible experimental realization and detection of the force in future experiments.

Europhysics Letters (EPL)•Jan 1, 2009•9 citations

Repulsive Casimir force in Bose–Einstein Condensate

Mir Mehedi Faruk, Shovon Biswas

Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.

arXiv:1712.08200•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2018•17 citations
Recently, the Casimir pressure was calculated for infinitely thin and infinitely repulsive parallel plates due to quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate (BEC). We generalize this result and obtain an expression for the Casimir pressure in a three-dimensional rectangular cavity with Dirichlet boundary conditions and arbitrary lengths. We then calculate finite size corrections to the parallel plate scenario.
The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.
Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.
We discuss a Casimir force due to zero-temperature quantum fluctuations in an interacting quasi–one-dimensional Bose-Einstein condensate (BEC). For the first time, we can investigate the effect of the trapping potential and the atom-atom interaction simultaneously both of which contribute to the Casimir force. Furthermore, we calculate the Casimir force due to thermal fluctuations at finite temperature. Finally, we speculate on some possible experimental realization and detection of the force in future experiments.
Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.